**Department of Mathematics**

**A
Dilation Theorem For Invariant Weakly Positive Semidefinite Kernels Valued
In Admissible Spaces**

**SERDAR AY**

**(BILKENT UNIVERSITY)**

**Abstract:** An ordered *-space Z is a complex vector space with a conjugate linear
involution *, and a strict cone Z+ consisting of self-adjoint elements. An
admissible space in the sense of Loynes is an ordered *-space with a complete
locally convex topology, compatible with the
partial ordering of its cone. We consider weakly positive semidefinite
kernels that are invariant under a left action of a *-semigroup and valued in
an admissible space. Under a suitable boundedness condition we obtain VH
(Vector Hilbert) space linearisations and equivalently, reproducing kernel
VH-spaces and *-representations of the *-semigroup on them. As applications of
the

main theorem, we obtain various known dilation theorems with a suitable choice
of a kernel and an admissible space. This is a joint work with A. Gheondea.

**Date: ****Thursday, November 24,
2016**

**Time: ****13:40**

**Place: ****Mathematics Seminar,
SA-141**

Tea and cookies will be served before the
seminar.